Explanation
To write a number as product of its primes, we divide it by various prime numbers 2, 3, 5, 7 etc one by one and check by which prime numbers it is divisible with and how many times.
Hence, 20 = 2 \times 10 = 2 \times 2 \times 5
The decimal expansion of a number is terminating if the denominator of the number can be expressed in the form of 2^m\times 5^n where m and n are non-negative integers
A) \dfrac{77}{210}, prime factorisation of the denominator is given as
210=2\times 3\times 5\times 7
\implies denominator is not of the form 2^m \times 5^n
B) \dfrac{23}{30}, prime factorisation of the denominator is given as
30=2\times 3\times 5
C) \dfrac{125}{441}, prime factorisation of the denominator is given as
441=21^2
D) \dfrac{23}{8}, prime factorisation of the denominator is given as
8=2^3
\implies denominator is of the form 2^m \times 5^n where m=3 and n=0
Hence the decimal expansion of \dfrac{23}{8} is terminating
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